To solve this we must first isolate the absolute value term which we can do by subtracting #color(red)(7)# from each side of the equation which will also keep the equation balanced:
#abs(3x + 6) + 7 - color(red)(7) = 28 - color(red)(7)#
#abs(3x + 6) + 0 = 21#
#abs(3x + 6) = 21#
The absolute value function and takes any negative or positive term and converts it into its positive form. Therefore we must solve the term within the absolute value function for both it's negative and positive equivalent.
Solution 1)
#3x + 6 = -21#
#3x + 6 - color(red)(6) = -21 - color(red)(6)#
#3x + 0 = -27#
#3x = -27#
#(3x)/color(red)(3) = -27/color(red)(3)#
#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = -9#
#x = -9#
Solution 2)
#3x + 6 = 21#
#3x + 6 - color(red)(6) = 21 - color(red)(6)#
#3x + 0 = 15#
#3x = 15#
#(3x)/color(red)(3) = 15/color(red)(3)#
#(color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3)) = 5#
#x = 5#
The solution to this problem is #x = -9# and #x = 5#
